few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Understand and apply the Pythagorean Theorem.

Understand and apply theorems about circles.

Prove geometric theorems.

Define trigonometric ratios and solve problems involving right triangles.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Experiment with transformations in the plane.

Reason with shapes and their attributes.

Solve real-world and mathematical problems involving area, surface area, and volume.

Make geometric constructions.

Understand similarity in terms of similarity transformations.

Classify two-dimensional figures into categories based on their properties.

Understand congruence in terms of rigid motions.

Explain volume formulas and use them to solve problems.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Translate between the geometric description and the equation for a conic section.

Prove theorems involving similarity.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Apply geometric concepts in modeling situations.

Find arc lengths and areas of sectors of circles.

Apply trigonometry to general triangles.

Analyze, compare, create, and compose shapes.

Use coordinates to prove simple geometric theorems algebraically.

Visualize relationships between two-dimensional and three-dimensional objects.
problem_activity: Task
Three of the great Egyptian pyramids are pictured below. Each is a square pyramid.
[IMG]
Calculate the missing information for each the 3 individual pyramids based on the given measurements:
The great Pyramid of Menkaure has a height of about 215 feet and a base side length of about 339 feet. What is its volume?
The great Pyramid of Khafre has a volume of about 74,400,000 cubic feet and a base side length of 706 feet. What is its height?
The great Pyramid of Khufu has a volume of about 86,700,000 cubic feet and a height of 455 feet. What is the length of its base?
The Great Pyramid of Khufu once stood 26 feet taller than it is today. Calculate the original volume of the Great Pyramid. Similarly, the Pyramid of Khafre has eroded over time and lost some of its height. If the original volume of the pyramid was approximately 78,300,000 cubic feet, what was its original height?


correct_option_index: 12